despite problems, difficulties, etc. 即使面对（问题、困难等）
She showed great courage in the face of danger.
面对危险她表现出了巨大的勇气。
while in a situation in which you have to deal with (something or someone that is dangerous, difficult, etc.)
Their defeat seemed certain in the face of such a powerful opponent.
面对如此强大的对手，他们的失败似乎毫无悬念。
She showed great courage in the face of danger. [=she showed great courage when she was faced with danger]
She succeeded in the face of [=despite] great difficulties.
尽管困难重重，她还是成功了。